Question

Triangle LMN has vertices at L(−1, 5), M(−1, 0), N(−2, 5). Determine the vertices of image L′M′N′ if the preimage is rotated 90° counterclockwise about the origin.
L′(5, 1), M′(0, 1), N′(5, 2)
L′(−1, −5), M′(−1, 0), N′(−2, −5)
L′(−5, −1), M′(0, −1), N′(−5, −2).
L′(1, −5), M′(1, 0), N′(2, −5)

Answer 1

To find the coordinates of the vertices of triangle LMN after a rotation of 90° counterclockwise about the origin, we can use the formula for rotating a point (x, y) by 90° counterclockwise, which is:

\[
(x', y') = (-y, x)
\]

We will apply this to each vertex of the triangle.

1. For vertex L(−1, 5):
\[
L' = (-5, -1)
\]

2. For vertex M(−1, 0):
\[
M' = (0, -1)
\]

3. For vertex N(−2, 5):
\[
N' = (-5, -2)
\]

Putting these transformed coordinates together, we get the new vertices after rotation:

- \( L'(-5, -1) \)
- \( M'(0, -1) \)
- \( N'(-5, -2) \)

This gives us the vertices of the image triangle L′M′N′ as:

- \( L′(-5, -1), M′(0, -1), N′(-5, -2) \)

Therefore, the correct answer is \( L′(−5, −1), M′(0, −1), N′(−5, −2) \).